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An ideal system of $n$ qubits has $2^n$ dimensions. This exponential grants power, but also hinders characterizing the system's state and dynamics. We study a new problem: the qubits in a physical system might not be independent. They can "overlap," in the sense that an operation on one qubit slightly affects the others. We show that allowing for slight overlaps, $n$ qubits can fit in just polynomially many dimensions. (Defined in a natural way, all pairwise overlaps can be $\leq \epsilon$ in $n^{O(1/\epsilon^2)}$ dimensions.) Thus, even before considering issues like noise, a real system of $n$ qubits might inherently lack any potential for exponential power. On the other hand, we also provide an efficient test to certify exponential dimensionality. Unfortunately, the test is sensitive to noise. It is important to devise more robust tests on the arrangements of qubits in quantum devices.

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Caltech Authors  

Autor(es)

Chao, Rui -  Reichardt, Ben W. -  Sutherland, Chris -  Vidick, Thomas - 

Id.: 70131475

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Tipo de recurso: Report or Paper  -  PeerReviewed  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] http://resolver.caltech.edu/CaltechAUTHORS:20171011-113818136
[References] https://authors.library.caltech.edu/82284/

Fecha de contribución: 12-oct-2017

Contacto:

Localización:
* Chao, Rui and Reichardt, Ben W. and Sutherland, Chris and Vidick, Thomas (2017) Overlapping qubits. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20171011-113818136

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